Bond diluted Levy spin-glass model and a new finite size scaling method to determine a phase transition

Abstract

A spin-glass transition occurs both in and out of the limit of validity of mean-field theory on a diluted one dimensional chain of Ising spins where exchange bonds occur with a probability decaying as the inverse power of the distance. Varying the power in this long-range model corresponds, in a one-to-one relationship, to change the dimension in spin-glass short-range models. Using different finite size scaling methods evidence for a spin-glass transition is found also for systems whose equivalent dimension is below the upper critical dimension at zero magnetic field. The application of a new method is discussed, that can be exported to systems in a magnetic field.

8 pages, 8 figures, 1 table

References in corpus (10)

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Cited by in corpus (10)

• Spin glasses in a field: Three and four dimensions as seen from one space dimension
• The correspondence between long-range and short-range spin glasses
• Imry-Ma criterion for long-range random field Ising model: short-/long-range equivalence in a field
• Finite-size critical scaling in Ising spin glasses in the mean-field regime
• The Ising M-p-spin mean-field model for the structural glass: continuous vs. discontinuous transition
• Novel disordering mechanism in ferromagnetic systems with competing interactions
• Numerical test of the replica-symmetric Hamiltonian for the correlations of the critical state of spin glasses in a field
• Infinite volume extrapolation in the one-dimensional bond diluted Levy spin-glass model near its lower critical dimension
• Spin glasses in a field show a phase transition varying the distance among real replicas (and how to exploit it to find the critical line in a field)
• Critical exponents of the spin glass transition in a field at zero temperature